Related papers: High-Dimensional Covariance Shrinkage for Signal D…
This paper considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to…
This work develops non-asymptotic theory for estimation of the long-run variance matrix and its inverse, the so-called precision matrix, for high-dimensional time series under general assumptions on the dependence structure including…
Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…
In many signal processing applications, including communications, sonar, radar, and localization, a fundamental problem is the detection of a signal of interest in background noise, known as signal detection [1] [2]. A simple version of…
We study high-dimensional sample covariance matrices based on independent random vectors with missing coordinates. The presence of missing observations is common in modern applications such as climate studies or gene expression…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…
One of the major challenges in multivariate analysis is the estimation of population covariance matrix from sample covariance matrix (SCM). Most recent covariance matrix estimators use either shrinkage transformations or asymptotic results…
In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…
We develop an asymptotic theory for $L^2$ norms of sample mean vectors of high-dimensional data. An invariance principle for the $L^2$ norms is derived under conditions that involve a delicate interplay between the dimension $p$, the sample…
The paper considers the problem of distributed adaptive linear parameter estimation in multi-agent inference networks. Local sensing model information is only partially available at the agents and inter-agent communication is assumed to be…
This paper deals with the problem of asymptotically optimal detection of changes in regime-switching stochastic models. We need to divide the whole obtained sample of data into several sub-samples with observations belonging to different…
The framework of this paper is that of adaptive detection in Gaussian noise with unknown covariance matrix when the training samples do not share the same covariance matrix as the vector under test. We consider a class of constant false…
We consider inference problems for high-dimensional (HD) functional data with a dense number (T) of repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal…
This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…
The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the…
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…
In this paper, we investigate the adequacy testing problem of high-dimensional factor-augmented regression model. Existing test procedures perform not well under dense alternatives. To address this critical issue, we introduce a novel…